1. Field of the Invention
The present invention relates to an electromagnetic wave analyzer apparatus which numerically analyzes the transitional behavior of electromagnetic waves, and more particularly, to an electromagnetic wave analyzer which treats a metal part as a medium having finite electrical conductivity.
2. Description of the Related Art
Today's computational electromagnetics exploits the Finite-Difference Time-Domain (FDTD) method as one of the techniques to analyze the transitional behavior of electromagnetic waves by using a computer for numerical calculation. This FDTD method, which solves the Maxwell's equations in the time and spatial domains using difference methods, is actually used in many different situations because of its wide scope of applications.
In a conventional FDTD-based electromagnetic wave analysis, researchers use either one of the following three techniques particularly when some metallic objects exist in the calculation space.
The first method performs computations on the assumption that every metal part in the calculation space is a perfect conductor that has an infinite electrical conductivity. Hereafter, this method is referred to as the "first conventional method."
In the first conventional method, an electrical wall boundary condition is set on the surface of a metal part as EQU E tan=0, (1)
where E tan represents an electric field component tangential to the metal part's surface.
This first conventional method is most popularly used, because it requires no computation about the electromagnetic field inside the metal parts. While being useful in many cases, this method is unable to handle such problems where the conductor losses in metal parts are not negligible. In order to solve this type of problems where the perfect conductor assumption is not applicable, it is necessary to introduce another computation algorithm that takes account of an electromagnetic field in a metal part, as will be described below.
The second method deals with the meshes corresponding to a metal part in the same way as those of other objects in the calculation space, while giving a finite electrical conductivity to that part. This method is referred to as the "second conventional method."
The second conventional method can analyze metal objects, taking their conductor losses into account by calculating electromagnetic fields inside of them. For further details of the above-described first and second conventional methods, see the publication of Kitamura et al., IEICE Transaction C-I, Vol. J76-C-I No. 5, May, 1993, pp. 173-180.
The second conventional method, however, has a disadvantage in the processing load imposed on computer platforms. That is, since the electromagnetic field exhibits exponential changes as it goes deep in a metal part, the spatial discretization intervals (or mesh size) must be set to much smaller values in that metal part, compared to those in other portions of the calculation space. Further, when the spatial discretization intervals are reduced, the temporal discretization intervals (or time step size) should also be reduced accordingly. This meshing strategy, however, will lead to a significant increase in both memory capacity and CPU time required for the computation. Therefore, still another calculation method that takes place of the second conventional method is demanded in order for an electromagnetic wave analysis to be conducted in a short time with limited hardware resources.
The third method sets a surface impedance boundary condition proposed by Beggs et al. on the surface of a metal part. Hereafter, this is referred to as the "third conventional method."
More specifically, when the x-axis is defined as an axis in the thickness-wise direction of a metal part, the frequency-domain steady state analysis of an electromagnetic wave Ey in a direction perpendicular to the x-axis is given by ##EQU1##
where .omega. is angular frequency, .mu. is permeability of the metal part, .sigma. is electrical conductivity, and j is the imaginary unit.
The time domain transient analysis by the FDTD method based on this expression (2) clarifies the transitional behavior of an electromagnetic wave. Besides eliminating the need for computation of electromagnetic fields inside the metal parts, this method enables the analysis to be executed taking the conductor loss into consideration. The details of this technique is available in the publication of J. H. Beggs et al., IEEE Transaction on Antennas and Propagation, AP40, No. 1, January 1992, pp. 49-56.
The above-described third conventional method uses Beggs's surface impedance boundary condition, assuming that the metal part has a sufficiently large thickness compared to the skin depth .delta., where .delta.=(2/.mu..sigma..omega.).sup.1/2. This assumption may be reversely interpreted as a drawback that the third conventional method cannot be applicable to such a case where the metal thickness is not sufficiently larger than the skin depth. This happens, for example, when a researcher tries to analyze the low frequency components of an electromagnetic field.